Abstract:The paper is devoted to the contributions of Coulomb and Amontons to the physics of friction from the viewpoint of current discussions and attempts to formulate generalized laws of friction.

This paper is devoted to an analytical, numerical, and experimental analysis of adhesive contacts subjected to tangential motion. In particular, it addresses the phenomenon of instable, jerky movement of the boundary of the adhesive contact zone and its dependence on the surface roughness. We argue that the “adhesion instabilities” with instable movements of the contact boundary cause energy dissipation similarly to the elastic instabilities mechanism. This leads to different effective works of adhesion when the contact area expands and contracts. This effect is interpreted in terms of “friction” to the movement of the contact boundary. We consider two main contributions to friction: (a) boundary line contribution and (b) area contribution. In normal and rolling contacts, the only contribution is due to the boundary friction, while in sliding both contributions may be present. The boundary contribution prevails in very small, smooth, and hard contacts (as e.g., diamond-like-carbon (DLC) coatings), while the area contribution is prevailing in large soft contacts. Simulations suggest that the friction due to adhesion instabilities is governed by “Johnson parameter”. Experiments suggest that for soft bodies like rubber, the stresses in the contact area can be characterized by a constant critical value. Experiments were carried out using a setup allowing for observing the contact area with a camera placed under a soft transparent rubber layer. Soft contacts show a great variety of instabilities when sliding with low velocity — depending on the indentation depth and the shape of the contacting bodies. These instabilities can be classified as “microscopic” caused by the roughness or chemical inhomogeneity of the surfaces and “macroscopic” which appear also in smooth contacts. The latter may be related to interface waves which are observed in large contacts or at small indentation depths. Numerical simulations were performed using the Boundary Element Method (BEM).

Abstract:The present paper is devoted to a theoretical analysis of sliding friction under the influence of oscillations perpendicular to the sliding plane. In contrast to previous works we analyze the influence of the stiffness of the tribological contact in detail and also consider the case of large oscillation amplitudes at which the contact is lost during a part of the oscillation period, so that the sample starts to "jump". It is shown that the macroscopic coefficient of friction is a function of only two dimensionless parameters-a dimensionless sliding velocity and dimensionless oscillation amplitude. This function in turn depends on the shape of the contacting bodies. In the present paper, analysis is carried out for two shapes: a flat cylindrical punch and a parabolic shape. Here we consider "stiff systems", where the contact stiffness is small compared with the stiffness of the system. The role of the system stiffness will be studied in more detail in a separate paper.

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We study theoretically and numerically the kinetics of the coefficient of friction of an elastomer due to abrupt changes of sliding velocity. Numerical simulations reveal the same qualitative behavior which has been observed experimentally on different classes of materials: the coefficient of friction first jumps and then relaxes to a new stationary value. The elastomer is modeled as a simple Kelvin body and the surface as a self-affine fractal with a Hurst exponent in the range from 0 to 1. Parameters of the jump of the coefficient of friction and the relaxation time are determined as functions of material and loading parameters. Depending on velocity and the Hurst exponent, relaxation of friction with characteristic length or characteristic time is observed.

There is a global tendency to rejuvenate joint diseases, and serious diseases such as arthrosis and arthritis develop in 90% of people over 55 years of age. They are accompanied by degradation of cartilage, joint deformities and persistent pain, which leads to limited mobility and a significant deterioration in the quality of life of patients. For the treatment of these diseases in the late stages, depending on the indications, various methods are used, the most radical of which are methods of joint arthroplasty and, in particular, total arthroplasty. Currently, total arthroplasty is one of the most effective and high-quality surgical operations at the relevant medical indications. However, complications may also arise after it, leading, inter alia, to the need for repeated surgical intervention. In order to minimize the likelihood of complications, the artificial joints used in total arthroplasty and the technology of their fabrication are constantly being improved, which leads to the emergence of new designs and methods for their integration with living tissues. At the same time, at the moment, the improvement of traditional designs and production technologies has almost reached the top of their art, and their further improvements can be insignificantly or are associated with the use of the most up-today technologies, allowing for friction couples with low tribological properties to provide for them high ones, for example, gradient increase hardness in the couple titanium alloy on titanium alloy. This paper presents the current state of traditional technical means and technologies for joint arthroplasty. The main attention is paid to the analysis of the latest technologies in the field of joint arthroplasty, such as osseointegration of artificial joints, the improvement of materials with the property of osteoimmunomodulation, the improvement of joint arthroplasty technologies based on the modeling of dynamic osteosynthesis, as well as the identification of possible unconventional designs of artificial joints that contribute to these technologies, predictive assessment of areas for technologies improvement.

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